Statically and dynamically balanced oscillator based on Watt's linkage

We present a new mechanical oscillator architecture that can be made insensitive to linear and angular accelerations while keeping constant oscillation frequency. The oscillator has the kinematics of a Watt linkage, so we call it a Watt oscillator. In order to predict its behaviour when it is subjected to external forces, we propose an analytical model using simplifying hypotheses. The solutions given by the analytical model were tested using an FEM model in order to obtain a dynamically balanced mechanism with frequency insensitive to external forces. A satisfactory correspondence between theory and FEM was found.

Theory and design of spherical oscillator mechanisms

Roland Andreas Bitterli, Nicolas Ferrier, Simon Nessim Henein, Mohammad Hussein Kahrobaiyan, Billy Nussbaumer, Lennart Rubbert, Ilan Vardi

In previous work, we showed that two degree of freedom oscillators can be advantageously applied to horological time bases since they can be used to eliminate the escapement mechanism. We subsequently examined planar two degree of freedom oscillators based on parallel flexure stages. We noted that these oscillators are strongly affected by the orientation of gravity so are not directly suitable for portable timekeepers such as wristwatches. In this paper we examine the design and performance of two degree of freedom spherical oscillators. By spherical oscillator, we mean a spherical mass having purely rotational kinematics and subject to elastic restoring torque. As opposed to our previously examined oscillators, the oscillation period of spherical oscillators is relatively insensitive to the effect of tilting the mechanism in the presence of gravity. In order to restrict spherical rotation to two degrees of freedom, we restrict the kinematics to obey Listing's law, a well–known constraint occurring in human eye movement. We show that a particular central restoring force we call the scissors law is best suited for chronometric performance and propose a number of theoretical mechanisms producing it. We then design an actual spherical oscillator based on our theoretical results. The design uses flexure springs to restrict kinematics to Listing's Law, produce the scissors law and provide the necessary suspension. Finally, we present experimental data based on a physical realization indicating promising chronometric performance.

Elsevier2018

Flexure Pivot Oscillator With Intrinsically Tuned Isochronism

Simon Nessim Henein, Mohammad Hussein Kahrobaiyan, Etienne Frédéric Gabriel Thalmann, Ilan Vardi

The most important property for accurate mechanical time bases is isochronism: the independence of period from oscillation amplitude. This paper develops a new concept in isochronism adjustment for flexure-based watch oscillators. Flexure pivot oscillators, which would advantageously replace the traditional balance wheel-spiral spring oscillator used in mechanical watches due to their significantly lower friction, exhibit nonlinear elastic properties that introduce an isochronism defect. Rather than minimizing this defect, we are interested in controlling it to compensate for external defects such as the one introduced by escapements. We show that this can be done by deriving a formula that expresses the change of frequency of the oscillator with amplitude, i.e., isochronism defect, caused by elastic nonlinearity. To adjust the isochronism, we present a new method that takes advantage of the second-order parasitic motion of flexures and embody it in a new architecture we call the co-RCC flexure pivot oscillator. In this realization, the isochronism defect of the oscillator is controlled by adjusting the stiffness of parallel flexures before fabrication through their length Lp, which has no effect on any other crucial property, including nominal frequency. We show that this method is also compatible with post-fabrication tuning by laser ablation. The advantage of our design is that isochronism tuning is an intrinsic part of the oscillator, whereas previous isochronism correctors were mechanisms added to the oscillator. The results of our previous research are also implemented in this mechanism to achieve gravity insensitivity, which is an essential property for mechanical watch time bases. We derive analytical models for the isochronism and gravity sensitivity of the oscillator and validate them by finite element simulation. We give an example of dimensioning this oscillator to reach typical practical watch specifications and show that we can tune the isochronism defect with a resolution of 1 s/day within an operating range of 10% of amplitude. We present a mock-up of the oscillator serving as a preliminary proof-of-concept.

2020

Flexure Pivot Oscillator With Intrinsically Tuned Isochronism

Simon Nessim Henein, Mohammad Hussein Kahrobaiyan, Etienne Frédéric Gabriel Thalmann, Ilan Vardi

2020